Instabilities of Hexagonal Patterns with Broken Chiral Symmetry

Details Instabilities of Hexagonal Patterns with Broken Chiral Symmetry Instabilities of Hexagonal Patterns with Broken Chiral Symmetry

1999-06-07

arxiv.org/abs/patt-sol/9906008v1

Nonlinear Sciences

Pattern Formation and Solitons

11 pages, 7 figures, submitted to Physica D

Scientific paper

10.1016/S0167-2789(99)00212-2

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and oscillatory, long- and short-wave instabilities of the hexagons are found. For the long-wave behavior coupled phase equations are derived. Numerical simulations of the Ginzburg-Landau equations indicate bistability between spatio-temporally chaotic patterns and stable steady hexagons. The chaotic state can, however, not be described properly with the Ginzburg-Landau equations.

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